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Following a week of seesaw talks and rising tensions between Republicans and Democrats over allegedly broken deals, Lt. Gov. David Dewhurst said he expects the House and Senate to finally agree Friday on a new state budget that would restore $4 billion of historic spending cuts to public schools two years ago.

That is the biggest give-back to schools on the bargaining table at any point during this 140-day session, where time and money are both running out. Only one full week at the Capitol remains for lawmakers, and to make this deal and numbers work, a new wrinkle in the Senate offer divulged late Thursday calls for shaving $100 million from the budget.

What state agencies or programs would absorb those cuts was not yet known. But Dewhurst said the overall plan resolves all major issues with the House, where budget-writers were expected to regroup early Friday.

"We've written a good budget, and this makes it better," said Republican state Sen. Tommy Williams, the Senate budget chief.

Yet it's not the first time negotiators have predicted an imminent compromise. Williams and his House counterpart, Republican state Rep. Jim Pitts, had spoken with confidence of a midweek deal only to retreat back into offices and hash out new differences.

Dewhurst and Senate negotiators announced the latest apparent breakthrough late Thursday, shortly after emerging from lengthy closed-door talks and walking to the office of Democratic state Rep. Craig Eiland. House Democrats had begun the day fuming at Republicans, accusing them of reneging on earlier compromises and pulling money set aside from education at the last minute.

The latest proposal may satisfy House Democrats: It calls for putting another $200 million toward education, which Dewhurst and Williams said would raise the total of restored cuts to $4.07 billion. Two years ago, the Legislature slashed public school funding by $5.4 billion to close a massive budget shortfall, and Democrats have called restoring that funding their priority since January.

The proposal also spells out at least $1 billion in tax relief.

"It's a package deal," Dewhurst said.

Republicans also stand to score a political victory in the compromise: Williams said the deal would not bust the state spending cap, which House negotiators were willing to consider as talks stalled this month, but the Senate deemed forbidden.

Dewhurst and Senate negotiators left the Capitol shortly before midnight following a day of faint signs that a deal was in reach.

Budget leaders canceled meetings while House Democrats blasted the GOP and Gov. Rick Perry over allegations of sinking a deal behind the scenes and lobbing political threats.

Rep. Sylvester Turner, emerging from a caucus of House Democrats, had blamed Republicans for reneging on a deal that had called for putting an extra $3.9 billion back into public schools, which absorbed historic spending cuts two years ago.

"For anyone to represent that Democrats have changed their position or asked for more is absolutely not true," Turner said. He went on to accuse Perry of swooping in late and telling Republicans not to vote for an agreed-upon plan because too much was being spent on reversing public school cuts.

Perry wants $1.8 billion in tax cuts and a new $2 billion water fund, but money is running tight and time running out. One $500 million bump the House already approved for classrooms, Turner said, was now being targeted to pay for highway projects instead.

Perry responded by saying he was "not going to participate" with those he described as trying to create conflict in the waning days of what has been -- until now -- a largely and unexpectedly harmonious session. Aides to Perry also denied that he told GOP members not to vote on an earlier budget proposal.

"I'm sure that there are folks that would like to blow up the session just to see the pieces of the machinery blow up through the air," Perry said.

Democrats have 55 votes in the 150-person chamber. Without their support, the House cannot reach the two-thirds threshold necessary to draw $2 billion from the state's Rainy Day Fund in order to jump-start an aggressive, bipartisan plan for new water projects across the state.